Reversed digits problem
Did you know that 12 X 42 = 21 X 24?
Can you find all the other pairs of 2 digit numbers where the product stays the same when the digits are reversed?
(Hint: Think about a strategy for finding them rather than just trying out lots of numbers.)
Imagine we have a pair of 2 digit numbers – let us call them 10a+b and 10c+d, where a and c are whole numbers less than 10.
Then we want the following to be true:
(10a+b)(10c+d) = (10b+a)(10d+c)
When we multiply this out we find that ac=bd, meaning that when we multiply the tens digits of the two numbers together this must equal the unit digits multiplied together, giving 28 possible pairs of two digit numbers.
Image credit Vin on the move